Hilbert’s Nullstellensatz
Published:
We record a proof of the bijection of algebraic sets and radical ideals, using Hilbert’s Nullstellensatz.
Posts by Tags
algebraic geometry
automorphism
Groups With No Automorphisms
Published:
We classify the groups with trivial automorphism groups. This was a pretty tricky problem on my girlfriend’s algebra qualifying exam the other day!
field theory
Automorphisms of Fields
Published:
We describe some rigidity (or lack thereof) results for field automorphisms. This is based on another problem from my girlfriend’s algebra exam.
filters
Tychonoff’s Theorem via Filters
Published:
To give myself some practice with filters, we describe the proof of Tychonoff’s theorem via filters.
finite fields
The Sign of the Linear Action
Published:
We compute the sign of \(\operatorname{GL}_n(\mathbb F_q)\) acting on \(\mathbb F_q^{\oplus n}\).
group theory
The Sign of the Linear Action
Published:
We compute the sign of \(\operatorname{GL}_n(\mathbb F_q)\) acting on \(\mathbb F_q^{\oplus n}\).
Groups With No Automorphisms
Published:
We classify the groups with trivial automorphism groups. This was a pretty tricky problem on my girlfriend’s algebra qualifying exam the other day!
nets
Nets
Published:
For my own personal use, we review the basic theory of nets.
nullstellensatz
Hilbert’s Nullstellensatz
Published:
We record a proof of the bijection of algebraic sets and radical ideals, using Hilbert’s Nullstellensatz.
permutations
The Sign of the Linear Action
Published:
We compute the sign of \(\operatorname{GL}_n(\mathbb F_q)\) acting on \(\mathbb F_q^{\oplus n}\).
polynomials
Units in Polynomial Rings
Published:
We classify the units in polynomial rings.
ring theory
Hilbert’s Nullstellensatz
Published:
We record a proof of the bijection of algebraic sets and radical ideals, using Hilbert’s Nullstellensatz.
Units in Polynomial Rings
Published:
We classify the units in polynomial rings.
topology
Automorphisms of Fields
Published:
We describe some rigidity (or lack thereof) results for field automorphisms. This is based on another problem from my girlfriend’s algebra exam.
Tychonoff’s Theorem via Filters
Published:
To give myself some practice with filters, we describe the proof of Tychonoff’s theorem via filters.
Nets
Published:
For my own personal use, we review the basic theory of nets.
tychonoff
Tychonoff’s Theorem via Filters
Published:
To give myself some practice with filters, we describe the proof of Tychonoff’s theorem via filters.
units
Units in Polynomial Rings
Published:
We classify the units in polynomial rings.